Answer :
Final answer:
The weight of peanuts in the mixture is 8 kg and the weight of corns in the given mixture = 4 kg
Explanation:
A mixture of peanuts and corn sells for P40 per kilo.
Let us assume the weight of peanuts in the mixture = x kg
The weight of corn in the given mixture = y kg
Total weight = (x + y) kg
The combined mixture weight = 12 kg
= x + y = 12 ..... (1)
Cost of per kg if mixture = $ 40
So, the cost of (x + y) kg mixture = (x+y) 40 = 40(x+ y) ..... (2)
The cost of 1 kg of peanuts = $ 42
So cost of x kg of peanuts = 42 (x) = 42 x
The cost of 1 kg of corn = $ 36
So cost of y kg of corn = 36 (y) = 36 y
So, the total cost of x kg peanuts + y kg corns = 42 x + 36 y .... (3)
From (1) and (2):
40(x+ y) = 42 x + 36 y
x + y = 12 ⇒ y = 12 -x
Put this in 40(x+ y) = 42 x + 36 y
We get:
40(x+ 12 -x) = 42 x + 36 (12 -x)
480 = 42 x + 432 - 36 x
or, 480 - 432 = 6 x
or, x = 8
= y = 12 -x = 12 - 8 = 4
= y = 4
Answer:
The weight of peanuts in the mixture = 8 kg
The weight of corns in the given mixture = 4 kg
Step-by-step explanation:
Let us assume the weight of peanuts in the mixture = x kg
The weight if corns in the given mixture = y kg
Total weight = (x + y) kg
The combined mixture weight = 12 kg
⇒ x + y = 12 ..... (1)
Cost of per kg if mixture = $ 40
So, the cost of (x + y) kg mixture = (x+y) 40 = 40(x+ y) ..... (2)
The cost of 1 kg of peanuts = $ 42
So cost of x kg of peanuts = 42 (x) = 42 x
The cost of 1 kg of corns = $ 36
So cost of y kg of corns = 36 (y) = 36 y
So, the total cost of x kg peanuts + y kg corns = 42 x + 36 y .... (3)
From (1) and (2), we get:
40(x+ y) = 42 x + 36 y
x + y = 12 ⇒ y = 12 -x
Put this in 40(x+ y) = 42 x + 36 y
We get:
40(x+ 12 -x) = 42 x + 36 (12 -x)
480 = 42 x + 432 - 36 x
or, 480 - 432 = 6 x
or, x = 8
⇒ y = 12 -x = 12 - 8 = 4
⇒ y = 4
Hence, the weight of peanuts in the mixture = 8 kg
The weight of corns in the given mixture = 4 kg
